UC-NRLF 


ICAL  DRAWING 


r  COLLECTION  OF  PUTtS 
FOR  PRACTICAL  USE  IN 

ELEMENTARY 


MECHANICAL  DRAW! 

Xp 


O 


Q 


F.  Schraidt. 


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GIFT   OF 


^vCL  J 


GEOMETRICAL    DRAWING 

A  Collection  of  Plates   for  Practical  Use   in 

ELEMENTARY  MECHANICAL  DRAWING 


BY 

F.    SCHRAIDT,    M.    A. 

Head  of  the  Department  of  Drawing,  Oakland  High  School 

OAKLAND,    CALIFORNIA 


1915 
PUBLISHERS 

WHITAKER  AND  RAY-WIGGIN  CO. 

San  Francisco 


'V 


Copyrighted   1915  by 
WHITAKER  &  RAY-WIGGIN  CO. 


CONTENTS 


INTRODUCTION V 

LIST  OF  DRAWING  EQUIPMENT VI 

EXPLANATORY   NOTES VII 

PLATES 1-65 

GEOMETRICAL  DATA                 66 


310429 


INTRODUCTION 

Geometrical  Drawing  (Elementary  Mechanical  Drawing)  as  a  school  subject  comprises  a 
two-fold  purpose:  a  pedagogical  and  a  purely  practical  one.  A  pedagogical  benefit  lies  in  the 
training  in  regard  to  the  pupil's  accuracy  and  definiteness.  The  object  is  not  merely  to  rep- 
resent geometrical  figures  by  a  set  of  lines,  but  these  lines  must  be  closely  observed,  accurately 
measured  and  definitely  placed.  This  feature  of  discipline  must  always  be  kept  in  mind.  The 
plate  of  Geometrical  Drawing  is  also  to  develop  an  active  sense  for  symmetry  and  harmony;  the 
different  figures  and  problems  should  be  placed  so  as  to  balance  the  whole  outline.  The  general 
impression  of  the  finished  drawing  should  be  one  of  neatness,  expressed  in  line-work  and  letter- 
ing, and  of  cleanliness. 

While  this  purely  pedagogical  benefit  is  always  evident,  Geometrical  Drawing  is  particu- 
larly valuable  as  Elementary  Mechanical  Drawing  for  vocational  work,  be  it  for  mechanical 
or  structural  or  architectural  engineering.  Not  only  that  Geometry  and  the  "French"  Curve 
as  such  form  a  necessary  schooling  for  the  professional  draftsman  and  engineer,  but  the  student 
becomes  acquainted  in  this  work  with  his  mechanical  appliances,  as  scale,  T-square,  triangles, 
compass,  ruling  pen,  brush,  etc.  and  learns  their  proper  use.  With  this  knowledge  he  is  prepared 
to  handle  more  difficult  problems  of  drawing  since  he  has  previously  acquired  a  critical  eye  and 
a  trained  hand. 

Here  it  should  be  remembered,  that  the  nature  of  this  preparatory  drawing  in  regard  to  the 
choice  of  its  problems  is  not  so  important  as  the  exactness  in  the  line-work  itself.  A  student,  who 
has  acquired  a  sense  for  accuracy  and  habitual  neatness  is  well  prepared  for  his  professional 
work  because  he  has  learned  the  one  important  prerequisite,  namely :  how  to  make  any  drawing 
intelligent  and  reliable. 


VI 


LIST  OF  DRAWING  EQUIPMENT 

(A  SUGGESTION) 


1.  One  Drawing  Board,  about  16"  x  22". 

2.  One  24"  T-Square,  maple  blade,  walnut 

fixed  head, 
or  Transparent  Edges. 

3.  One  30°  Triangle,  about  10",  Transparent. 

4.  One  45°  Triangle,  about  8",  Transparent. 

5.  One  Triangular  Boxwood  Architect  Scale, 

12". 

6.  One  Set  of  Instruments,  consisting  of 

One  6"   Compass  with  Pen  and  Pencil 

Attachment. 
One  6"  Dividers. 
One  3y2"   Pen   Bow. 
One  5"  Ruling  Pen. 


7.    Two   Sheets  of   Cream   colored   Drawing 

Paper,   27"  x  40". 

This  size  of  paper  will  furnish  4  plates 
each.  If  good  quality  ("Duplex"  or 
"Corona")  is  selected,  it  will  take  ink 
well,  while  its  cream  color  does  not 
strain  the  eye  as  much  as  the  glaring 
white. 

One  A.  W.  Faber  Drawing  Pencil,  3Hr^ 
One    Pencil    Eraser,    E.    Faber    No.    Ill, 

green ;  One  Sponge  Eraser. 
Two    Bottles   Waterproof   Drawing   Ink, 

black  and  red. 
One    Dozen   thin   edge   Thumbtacks,    ffi' 

diam.  or  less. 
One  Penholder  with  Pens:  Esterbrook  & 

Co.  Interstate,  No.  815. 
One  Transparent  "French  Curve." 


8. 
9. 

10. 
11. 
12. 


13. 


NOTE.— It  is  suggested,  that  no  Ink  Eraser  or  Knife  be  used  for  corrections  in  ink. 
green  Pencil  Eraser  with  the  application  of  a  little  powdered  Pumice  will  do  neater  work. 
Equipment  not  available  in  local  stores  can  be  ordered  from  the  publishers. 


The 


VII 


EXPLANATORY  NOTES 

The  following  sixty-five  pages  represent  a  set  of  sixty  practical  plates  for  Geometrical  or  Ele- 
mentary Mechanical  Drawing  for  Secondary  and  Primary  Schools.  From  these  the  instructor  or 
student  is  to  select  a  number  of  plates  according  to  requirement  or  taste.  A  set  of  twenty-five 
plates  is  suggested  as  equivalent  to  a  school  year's  work  with  one  daily  period  or  forty-five  minutes, 
or  to  half  a  year's  work  with  double  periods  daily.  The  consecutive  number  of  each  chosen  plate 
may  be  inserted  in  the  space  provided  for. 

The  size  of  each  plate  which  the  student  is  to  make  from  the  small  sample  drawing,  is 
assumed  to  be  12"  x  17",  and  good  cream  colored  or  white  drawing  paper  should  be  used;  the 
margin,  represented  by  a  heavy  line,  allows  a  space  of  one  inch  on  each  side.  Each  sample 
plate  in  this  book  has  been  furnished  with  dimensions  measuring  from  the  margin  line,  which 
will  place  the  problems  well  on  the  sheet.  The  student  observes,  how  a  drawing  might  prop- 
erly be  provided  with  dimensions;  yet,  he  is  asked  to  omit  the  same  from  his  plate,  since  this  is  a 
feature  of  Mechanical  Drawing  proper  and  not  included  in  the  present  course. 

The  sample  plates  are  drawn  "to  scale,"  but  at  a  reduced  size ;  therefore  the  student  will  find 
it  impossible,  simply  to  measure  off  from  the  sample  any  dimension  with  the  dividers.  In  case 
a  dimension  should  not  readily  be  found  on  the  plate,  the  student  will  have  to  compute  or  to 
calculate  by  proportion  the  desired  length. 

A  possible  objection,  that  the  student  is  merely  "copying"  a  plate  is  not  justified;  he  is  repro- 
ducing a  drawing  of  his  own,  using  a  good  and  correct  sample,  and  since  "Mechanical"  Drawing 
requires  a  number  of  mechanical  tools  and  skill  in  using  them,  it  might  well  be  said,  that  in 


VIII 


the  elementary  work  of  this  sort  emphasis  be  laid  on  the  acquaintance  with  these  tools  and  with 
their  possibilities.  The  process  of  making  a  Mechanical  Drawing  in  regard  to  forming  a  habit 
of  good  line  work  must  become  an  unconscious,  a  mechanical  one  by  repeated  practice,  before  the 
student  can  pay  all  attention  to  advanced  problems  of  design  and  construction. 

Neat  lettering  should  receive  special  attention,  and  each  plate  should  be  valued  in  regard 
to  careful  lettering  as  well  as  to  its  line  work;  special  "lettering  plates,"  a  practice  in  Free- 
hand printing,  should  be  made  from  time  to  time. 

It  is  essential  for  the  development  of  carefulness  and  skill  to  use  ink  after  the  plate  has 
been  completed  in  pencil ;  waterproof  black  ink  is  recommended  for  the  heavy  lines,  and  red  ink 
for  the  fine  construction  lines.  If  a  variety  of  colored  inks  is  preferred,  there  should  be  a  uni- 
form system  carried  on  throughout  the  whole  course. 

Individual  taste  can  well  be  taken  into  consideration,  and  changes  on  the  suggested  plates 
be  made  accordingly. 

Explanation   of   signs:     R=Radius;    Z.=Angle;    ||=Parallel;     |  =Vertical. 
Pages  1,  2,  3,  and  4  offer  exercises  in  simple  line  work  with  the  T-square  and  both  triangles. 
Page  5  condenses  the  practice  of  several  previous  pages  into  one  plate. 

Pages  6  and  7  contain  simple  straight  line  designs,  which  might  also  be  used  for  practice  in 
flat  tinting.  . 

Page  8  shows  block  letters,  filled  in  with  black  ink;  but  any  water  color  could  be  used  instead. 

Pages  9,  10,  11,  12,  13,  14,  15,  16,  and  17  introduce  the  use  of  the  compass,  circles  alone  or  in 
connection  with  straight  lines. 

Pages  18,  19,  20,  21,  22,  and  23  deal  with  problems  of  Geometry. 


IX 


Page  18:  Each  Radius  (R)  on  this  page  is  arbitrary  in  length.  Line  A-B  of  the  fourth  prob- 
lem is  drawn  at  any  angle  and  of  any  length ;  beginning  at  A,  seven  equal  parts  of  any  size 
are  measured  off  on  this  line;  the  last  point  is  connected  with  C,  and  parallel  lines  to  this 
drawn  through  each  point  towards  A. 

Page  19 :  In  order  to  solve  the  sixth  problem,  A-B  is  bisected  in  C,  an  arc  is  drawn  to  E  with 
R=C-D,  and  another  arc  with  R=D-E  to  find  F.  D-F  is  equal  to  one  side  of  the  Pen- 
tagon. 

Page  21  :  In  the  first  problem  bisect  P-C  in  A;  draw  a  circle  with  A  as  center  and  a  Radius= 
A-C  and  mark  the  points  of  intersection  with  the  given  circle.  Connecting  P  with  these 
points  will  furnish  the  tangents.  . 

In  the  second  problem  bisect  A-B  in  C ;  the  arc  with  A-C  as  Radius  intersects  the  arcs 
with  Radius  of  B  plus  or  minus  Radius  of  A  in  point  D.  A  parallel  line  to  A-D  at  a  dis- 
tance equal  to  Radius  of  A  will  locate  the  two  points  of  tangency. 

In  the  third  problem  draw  arcs  around  A  with  a  Radius^R  of  A  plus  R  of  C  and 
around  B  with  a  Radius=  R  of  B  plus  R  of  C,  and  find  center  for  C  at  intersection. 

Problems  four  and  five  are  solved  by  adding  to  or  subtracting  from  line  P-C  the  Radius 
of  B.  The  bisecting  perpendicular  of  P-B  will  meet  the  production  of  P-C  in  D,  the  cen- 
ter for  the  required  circle. 

In  the  sixth  problem  draw  arcs  with  R=A-C  as  shown,  connect  D  with  C,  which  inter- 
sects the  perpendicular  of  A-C  in  E;  measure  off  the  distance  of  A-C,  beginning  in  E, 
three  times  and  find  H.  H-B  is  equal  to  one-half  of  the  circumference. 

Page  24  contains  simple  circle  designs,  applying  problem  four  on  page  18  and  problem  six  on  page 
19. 


Pages  25,  26,  27,  and  28  show  different  designs  for  flat  tinting  in  one  or  in  different  colors. 
Only  first-class  water  colors  and  good  brushes  should  be  used.  The  sections  of  Standard 
Profile  Steel  on  page  28  are  taken  from  the  catalog  of  Jones  &  Laughlin,  Steel  Company, 
Pittsburg.  The  pounds  (tt>)  indicated,  refer  to  weight  of  steel  per  foot. 

Page  29   includes   compass   curves  and   an   exercise  in  "French"  curves. 

Pages  30  and  31,  showing  the  Spiral,  Involute,  and  Volute,  are  drawn  with  the  compass.  The 
Spiral  on  the  right  side  of  page  30,  however,  is  also  drawn  with  the  "French"  curve.  The  In- 
volute is  obtained  by  drawing  arcs  with  Radii  from  1,  2,  3,  4,  etc.,  on  the  circumference 
of  the  given  circle,  to  the  tangent  of  each  corresponding  point.  The  Involute  is  applied  in 
Gearing;  the  Volute  is  an  architectural  ornament. 

Pages  32,  33,  and  34,  showing  curves  formed  by  straight  lines,  are  suggested  as  introduction  to 
the  curves  proper. 

Page  35  presents  methods  to  obtain  a  Parabola  and  a  Hyperbola. 

Pages  36,  37,  and  38  are  devoted  to  the  Ellipse.  The  "Trammel,"  cut  out  from  paper,  on  page 
36  moves  with  its  two  given  points  on  C-D  and  A-B  respectively,  thus  outlining  at  its  outer 
end  the  Ellipse.  The  "Focus"  of  the  Ellipse  on  page  38  is  found  by  an  arc  with  a  Radius= 
one-half  of  the  Major  Axis.  With  one  Focus  as  center  and  any  Radius  larger  than  the 
distance  from  the  Focus  to  the  nearest  end  of  the  Major  Axis  (in  this  case  1"  has  been 
chosen)  draw  an  arc;  with  the  other  Focus  as  center  and  a  Radius=Major  Axis  minus 
the  chosen  Radius  of  the  first  arc  (1")  draw  another  arc;  both  arcs  will  interect  and  lo- 
cate two  points  for  the  Ellipse;  repeat  this  process  any  number  of  times  with  new  dimen- 
sions. The  second  problem  on  page  38  is  suggested  as  an  example  for  drawing  a  Circle 


XI 


in  Isometric  Projection,  where  it  becomes  an  Ellipse.  Draw  Square  within  Circle  first, 
then  30°  line  with  divisions  as  shown.  The  distance  marked  X  is  obtained  with  the  divider 
from  the  circle  construction  and  measured  down  from  the  30°  line  for  the  Ellipse. 

Pages  39,  40,  and  41  contain  the  three  Conic  Sections,  which  will  produce  the  Hyperbola,  the 
Parabola,  and  the  Ellipse.  The  angles  of  45°  and  60°  have  been  chosen  for  the  sake  of 
convenience  and  do  not  necessarily  have  to  be  of  this  size. 

Pages  42,  43,  44,  and  45  show  examples  of  the  Cycloid,  the  Epicycloid,  and  the  Hypocycloid. 
These  curves  are  traces  of  a  point  on  a  circle  rolling  on  a  straight  line  or  on  another  circle. 
The  equal  distances  marked  1,  2,  3,  4,  etc.,  on  the  given  circle,  which  is  drawn  first,  are 
measured  off  from  both  sides  of  its  center  line  on  the  straight  line  or  the  circle,  on  which 
the  first  circle  is  to  roll. 

Cycloids  are  frequently  used  in  Gearing. 

Page  46  represents  the  Helix,  a  curve,  which  rer.embles  the  path  of  a  point  uniformly  moving 
around  on  the  circumference  of  a  cylinder  and  at  the  same  time  on  the  surface  of  the 
cylinder  along  a  line  parallel  to  its  axis.  The  vertical  distance,  which  is  the  point  has 
moved  along  this  line,  is  called  the  "Pitch";  Pitch  and  circumference  of  the  Cylinder  must 
always  be  drawn  first  to  determine  the  points  of  construction  for  the  Helix,  and  both  are 
divided  into  the  same  number  of  equal  parts.  In  order  to  save  space,  only  one-half  of  the  cir- 
cumference of  the  Cylinder  is  shown  in  each  case. 

Pages  47  and  48  give  examples  of  the  Helix  as  a  curve  of  different  screw-threads.  The  very 
ends  at  the  turn  of  each  curve  are  best  drawn  with  a  compass,  being  too  small  for  the 
"French"  curves. 

Page  49  shows  a  symmetrical  arrangement  of  "French"  curves. 
Page  50  gives  the  construction  of  a  truly  Egg  shaped   Oval. 


XII 


Pages  51  and  52  submit  a  practical  application  of  the  Ellipse  with  a  Major  Axis  of  29  and  a 
Minor  Axis  of.  18  feet.  This  Ellipse  should  be  constructed  first  followed  by  the  23"  divisions, 
beginning  at  each  end  of  the  curve  towards  the  middle,  and  tangent  to  an  arc  drawn  at  each 
division  point  with  a  Radius  of  24"  is  drawn  the  second  and  outer  Ellipse.  The  slanting 
lines — between  these  two  curves — are  drawn  from  the  point  of  tangency  to  the  division 
point  on  the  inner  Ellipse.  Note  the  use  of  a  Scale:  jM$"=l  foot,  which  will  be  found  on 
each  triangular  Architect's  Scale. 

Pages  53  and  54  are  dealing  with  problems  to  locate  the  path  of  motion  of  a  point,  which  will 
be  found  to  travel  on  an  irregular  curve,  returning  to  its  starting  point. 

Page  55  shows  examples  in  Shading.  Note  that  with  a  darker  tone  of  shadow  the  shading  lines 
become  narrower  and  heavier. 

Page  56  contains  in  outlines  three  important  cases  of  Projection.  Since  this  topic  is  treated 
largely  in  the  second  part  of  this  work  called  "Descriptive  Geometry,"  no  further  details 
or  applications  are  given  here. 

Pages  57,  58,  59,  60,  61  and  62  give  three  samples  of  Gothic  design.  The  sheets  showing  the 
construction  method  in  each  case,  will  furnish  sufficient  explanation. 

Page  63  shows  a  Balustrade  with  an  application  of  plain  surface  shading.  Note  the  Scale: 
\l/2"=\  Foot,  found  on  the  triangular  Architect's  Scale. 

Pages  64  and  65  suggest  an  alphabet  of  shaded  letters.  Instead  of  the  black  shadow  each  letter 
might  receive  a  light  coat  of  water-color  and  the  shaded  part  of  it  be  painted  in  a  darker 
tone  of  the  same  color. 

Page  66  contains  some  geometrical  data,  which  might  be  convenient  when  computing  various 
dimensions  for  geometrical  figures. 


PL  ATE  \       I 


K 

/— 


s 


PLATE 


IZL 


Note  :  Omif  a//  rf/'/nens/ons. 


PLA  TE  O 


Note  :  Omit  a//  dimensions. 


P/ATF\       I 


/Vote  .-  Orrtif  a//  d/mens/ons 


.•  Omtt 


PLATE\      I 


6 


Om/f  c/t'mensions   and  construcf/on  /fries 


PLATED 


Nofe ••   Om/'f  d/mensions    and     construct/online s. 


8 


Nofe:  Omit  a/t  dim  en  si  on  s  and  consfrt/ctton  fines. 


PLATE\       I 


//<?/«• .-  O/rtff  a//  d/mens/ons. 


10 


Nofe  ••  Om/'f  a//  cf/'m  en  s/'ons. 


PLATE  I      I 


11 


/Vofe  ••  Omif  all  cf/menstons. 


PLATE 


12 


Nofe  ••  Om/'f  a//  d/mens/ons 


13 


Drawn  n>/S/7  ffif    Compass. 


Oral 
Dron-f?   rvtfh  /fte  Compass. 


:  Omit  d/mens/ony ,  bcsf pror/de    constrtscftorr  /r>  fine  reef  //nes 


PLATE\      I 


/Vo/e     Omif   d/mens/ons     ar?  rf  co/~isfrcrcf/on   /tries 


PLATED 


Nofe    Om/f  tf/mens/ons ,  £>i/f  f>ror/c/e  cof-j sfrc/cf/on  tr?  f/ne 


PLATE 


16 


Show  construe/ion   in  f/ne  fines  on  /eff  side  of  p/ate  asa&ore;  om/f  dimensions. 


PLATED 


17 


A/o/e  •    Omff    di'mens/'ons     one/    consfr<scf/on//n9S. 


PLATE\      I 


To   butct  a\fiftn/t'nt 


To  draw  a /atr/oendicu/arat /he  end 
of  a  gfven  line  . 


/\ 


To  dra*  a  perpend icu/ar  to  a 
given  /int  from  a  point  P 


To  cfiric/m    a  yirtn  //>?«    info 
any  number  ofcpva/  parts  . 


To   bi'secf   a  tfirtn  a  not*. 


/Vott :  Pror/de   a/I  printing  as  shown  abore,  buf  omif  dimensfons. 


PLA7E 


To  /riser/be  an  «<fcf/7af9fa/  tr/ana/e 
rvtffti'n  a  yt'ven  cire/t . 


75  /mcr/Ae  a  square  iviffi/'n  a 
y/r  */7   ctrc/e  . 


To  /nscrtbe  a  hexagon  Htithin    a 


To  co'nsfrucf   ahttaaon  on  a 
gfrtn    I  in  e  . 


75  conafri/ct  an  octagon    irithin 
a  y/'ren    sqe/ar*. 


To  fnscrttre   a  pentagon  ir'fftiri 
a^yfren    c/>c/r . 


A/ofe  ••  Omif  a// cf/menst'orrs,  but  prortde  jor/nf/nff;  3ma//  /effers  te>6e 


PL  ATE  \       I 


20 


To  inscr/t>e  a  circ/e    mrttriin 
on    eyw/afera/  fr/any/e  . 


To  /nscr/be  fhree   c/rc/fj  To  insert  60  /'our  circ/es 

fifrt/n  an   eo-<///afera/  fr/any/e.      nr/fh/n  art  eyt/'/artercr/  frfany/e 


To  /nscr/i>e    a  c/rc/e 
within  a  yr'ren    square. 


To   rrjscr/'Ae  foc//~    c/rc/es 
a   square   far>fer>f 
to    rtvff 


To  inscribe  four  circ/es 
a     square  fanyenf 
fo   one    sic/e  . 


Note--  Om/f  d/rner>y/onsj    but  pror/de    construction  in  f/ne  reef  //nes. 


PLATF\       I 


21 


To  draiv  tanyents  from  o    gtren 
po/rjf  fo  cr  ff/rer>     circ/e 


To  cfr  otY    a  fan  go  rtf   fo 
tno    9/ren    circles. 


To    draur    a   qfiren     cfrcle    C 
tangent   to  fno  offier  cfrctfs. 


To    efranr  a   circle   fangenrfo   ftvo    c/'rctey 
throtsgh    a  /oo/nf  art  //re   circumference    of  one 
of  the  y/ren    circ/es. 


circumference. 


To    /ap  ouf  fhf   cir 
of  a  yi'verr    c/rctf    as  a  straight  line. 


/Vofe  :  Omif  cltmens/orrs,  £>tsf prortcfe     consfrt/cf/or?  /rj  fine    reef  /in es. 


PL  A  T£\       I 


22 


7~o  consfrucf   a  po/ygon    of  any 
of  steles    f/n  this  case  7}  within  a 


>*>/-  To    consfrttcf  or  polygon    of  crny    number  of 

c/rc/e.  st'c/es  (ir?  fr>/-s  ccrse  7J  v pon  a  given  /ine  . 


. » 

Consfructfoni     A3-ZZ 
Ha/fcirc/e  nifk  R-AB 
B-l  *  1-1  ttc.  -*t>rArcBC 

Arc  BE-  relee. 

Lfn»  F6H 

Circ/e  nlfh  Cfntr-f  H,   R*  HB 
-BE  efc. 


A/ofe    Omit  cfimensforis,  6vf  pror/de  corufre/cf/on  tn  fine  reef  //nes,  fjf-inf/ny  Sr?  6/acA  in  ft. 


PLATE\      I 


23 


B  u  C  D  *ar6itrorf. 
FE  J.  A3.  SHJ.CO. 


To //not     fhe    centre  of 


f?  "  arbitrary 

To  trisect  an   any/e  of  4$* 


To  c/raiv    a  ffirert     c/rc/e 
fcrngenfto   frvo   rnfe 


//nes 


ft- arbitrary.      Cf'jCO 

£FJ.  AC     Arc  rw»  EG  to  H 

Art  nithHMteN 
Arc  nifhOH 


X,  AC  8-  arbitrary 
fi  '  arbitrary 
Arc  n/tti  2  f> 
Lint  FH      . 
'- 


LtnfS  /VC  B  fliC 


f  fit 

Tofrrsrcf  an   any/e  of  SO  * 


To    trisect  on  any/e  of  90  ' 


To  div/'de     any  any/e  infa 
any   number  of  equ a  I  f>arfs, 
in  this 


Note:   Om/'t  fj/rrtens/ons,  t>(sf  f>ror/c/e   corisfrt/cf/of-i  /'n  fine  red  /tne  s  crncf  jor/nt/ny  tn  t>/acje  ink 


24 


-  Omit    d/mens/ons     and    constrc/ ct/on  f/nes. 


25 


Des/yn  /or  f/a/     T/'nf/'rtg 


Omit    c/imens/ons     Use   2  or  more    cf/ffe rent 


P/ATE\       I 


26 


Des/yn  for  f/a/    77nt/'nff , 


/Vofe  ••  Omit  c//mens/'ons.  Use  2  or  more   cf/f/erent    co/ora. 


27 


Des/'gn    for 


7~/nf/ng. 


A/off.-  Omif  dimensions 


PLATED 


28 


CO 


Cross   -Sections  of  -Stanc/arc/    Profile    Jtee/. 

-*'->r-       -  a*'- 


IJ 

^ 

—  ^r- 

3i  "x3i"-IS.6 

[^ 

VV,                       .? 

" 


fl  "-  /<S#>.  -I-  Beam  . 


:  Orrt/'t  dimension  s,  t>ur /oror/c/e  jor/ntfrta.   &ire    cross   sections  aflat  tint  of  light 


29 


Tbconnecf    any  number  of  points  fin  this  case  7 J  with-  compass    ct/rrts 
The  y/rer>   dimensions  focafe  the  point's. 


Centre   for  f?  Cr?adit/s)  is  found  at 

intersection    of  perpendici//ar  bisector  between  fno 
jooinfs  and  extension  from  jorev/ovs  centre  through 

nearest  point 


Note  ••  Pror/cfe  constrvcf/on  lines   r'rt  upper   dronr/ny  y  omit  a/f  dimfns/orts. 


30 


Note  ••  Om/f  dimensions 


PLA  T£\      I 


Nofe  ••  Om/'f  dimensions,  but  prov/cte  conslrescfion  in  fine  red /ines,  pr/'nf/ny  and  ni/mera/s    in 

b/acfi . 


Ct/rres   formed    by  sfrajyht   tin 


/Vofe  :    Omif  d/mens/ons,  but  pror'de  constri/cfion  in  f/ne  red  lines-  numera/s   and 


in   f-i/rrrk 


PLAT£ 


33 


Curves  form  ecf  by   sfrcriyftf  //nes 


/Vofe  -•  Omit  d/merrs/ons,  buf  pror/de  constri/cfion   /n  f/'ne  reef  // 


j  numera/s  and  f>r/r)tir>y 
in  h/ac  A 


PLAT£\       I 


Cvrres    formed    Ay    straj'yht  ///->  es 


A/ofe:  Om/f  d/mens/ons,  t>uf  pro v/'afe   construcf/'on  in  fine  red  lines,  nt/m era/5   cr/7c/  pr/n//'ny 

/n  b/ack  . 


PLATE 


35 


/Vo/e  ••  Om/f  tf/mer?5/ons,  £>(/f  pror/de  cor?5fr(/cf/on  /r>  f/ne  red  fines 


36 


£Hipse 

Dratrn   wi/h  the  compass 
B 


by  means  of  a 
3 


MMJ.L6 
Line  N MO 
ArcKQ 
ArcQB 


'Vote  :  Om/t  d/mensfons,  but pror/de  construction  /n  f/ne  red //nes  and /or/nttny  /n  b/ack  ink . 


PL  ATE 


/Vo/e  :  Omi/  c/f'rnef7Sfor>5,  bvf  f>/-or/de  co/7 sfrocf/or>  /n  fine  reef //nes,  /it/rrt  era/s  in  b/ack  ink. 


PLATE\       I 


38 


C/rc/e      and    E/li/ose 


3_ 


/Vofe  :  Omif  d/mens/ons,  b(/f pro vr'c/e  cons1r</cf/or>  /n  ftne  red //nes;  nt/mer-a/& /'n  b/ack 


PLATE  \      I 


A/ofe  .-  O/77/f    G//s?-?er7S>o/7s ,  bi/f  prov/de    con  sfrt/ct/on  /'n  f/ne    reef  t/nes. 


PL  ATE 


A/ofe  :  Orri-if  of/me nsions ,  titsf  p>ror/c/e   construct/on  t'n  fine  reef  ///?<?  j. 


PLATE  \      I 


Nofe.-Omif      dimenj/ons ,  but pror/c/e    construction    in  fine    reef/ineS. 


///i/sf  ration   of  a     Cyc/or'cf . 


Om//  c//mer?s/or>s ,  £>tjf  pror/de  construct /'or?  of  cyc/o/'d  /n  f/r?e  reef,  //nes    erne/  rx/mera/s 
f'rr  6/ac/f  /r>k.     Om//-    cor? strvct/Ofi    on   /// u straf/on    ofcyc/o/d. 


PL  A 


Nofe :  Omit  dimensions,  buf  joror/cfe   construction  /n  f/'ne  reef  fines  and  numera/s  /n  black  ink. 


PLATE 


44 


Hyp  o  cy  c/o  fd 


ftadii    of  /argte  crfic/ 

sma//  whee/5  I'n  no  g/ven  proporf/on 
fo    each   other 


Radius    o/  s ma// 
^  rod/' us   of 


Note:   Omit  dimensions ,  t>ut  provide    consfruct/on    in  fine  red  fines. 


PL  A  TE\       I 


45 


Cpicycloid 


Ep/'  -  an  of   Hypo-  Cyc/o/d. 


/Vofe  ••  Omif  dimensions,  bt/f  provide    construction  in  fine  reef  fines 


PL  ATE  \      I 


Note:   Omit  d/mens/ons,  bi/f  pror/de  construct/on  //•?  fine  reef  //neat  r>t/mera/s  in  b/ack  /'nk 


I/"-  SfrcrpccS      Screir      7~/tr-eac/ 


A/o/e  :  Orr?/f  cf/snens/ons,  but  pror/cfe   construction  in  fine  red  //nes  and  nvmera/s  in  b/ack    ink. 


PLATE 


Sat/are      Screir      Threcra 


A/ofe.    Ofn/t  cf/mens/ons,  t>vf  prov/c/e   construct/on  /n  fine  reef   /fnesoncf  numera/s  in  ti/ack 


Prarcf/ce  in   frencrr     Curves. 


Wo/e  :  Omif  d/mens/on^ ,  bvf  pror/de   construction  in  f/ne  red  fines    For  construct/on 
d'/y/de    rad/c/s  /rtro  7  ar?d  c/'rcf/rrfferff^ce    r'f-?fo    ZZ    eae/ar/  /ocrrfs. 


Con  sfrtsc  f/on 

G/ron     AB-S".    CO  -  2  *AB 

Cf 
Bf-B'f  "  B"f~  etc    -AG'A'G 


Note:  Omt'f  et/mer>s/on}  best  pro  r/tfe 


PLATE\      I 


51 


Pracfic  a/  App//ca  f/o/7    of  /he  E////ose. 
(construct /on) 


Note  :  Omit   d/mens/ons    ana/  construction  //nes,     see  /o//ow/ng 
Use  JcaJe  :    4  "=  /foot 


PL  A  71  \       I 


52 


Practical  Application   of  an 


Note  :  /f  desired ,    gtre  br/dye    or  /~/a  t   tint   of  //'//?/   gray    co/or 


Pcrf/i    o/ mot/on     of  /aornf    D    dt/r/nf    one    rerefufion    around    crntrt   C 
A    moves    r/yht  and   /eft      on    ff    sffaf'yhf  tin*. 


A/ofe  :  Om/f    ctrmet-7  starts,  6<sf  /oror/c/e     cons frts c  f son    /n  reef 


PLATE\       I 


54 


of  mo f /on    of  po/nf  O  dur/rtg     one    rfyo/i/f/on    of  B  oroi/ne/    cerrfre    C. 
f^o/rrf   A    mores    r/ght    and    /eff     on      a      straight   line. 


Nofe :  Om/f  d/mens/ons,  b</f  /oror/afe    corvs/ruct/'on    /n  //ne    reef  //'nes. 


PLATE 


A/ofe  . 


5haaf/ng  //nes   /r?  t>/ack 


56 


Proje  cf/o  r>  s. 


Ho //civ    Cube . 
2"  square,  tva//s  g"  fht'ck 


Ob/ique  Pro/ecf/'on 

0n  2  of  J  A xes  -h or/2orrta/ 
and  verf/caf— dimensions 
are  measurec/  fu//  s/ze, 
on  fhe  ffit'rd  axfs-45*— 
the  dimensions  are  ha/f 
s/ze .. 


/somefr/c  Projection 

On  a//  three  Axes  -  one  verftccr/ 
fhe  of  her  fmo  af  3O°  to  fhe  rtori- 
zorj/cr/  /ine  —  a/f  (/imensfons 
are   rrifsurec/  fut/  Size. 


\ 

\ 

Hi 

ri'z 

onfaf  f>ro/ecfror 

ffo 

0   VI 

ft 

rff 

a/  Prty'ecfion  fj 

ran 

/  y/ 

f/'&w) 


Orff)O  <yrapft/c  fro/ecf/'on 
A//*vfeH's" of /rie  ob/ecf 
ore  pro/fefeef  yerfi'ca/fy 
from  one   /nfo  fhe  o/rier 
D/rnen3/0rr3  are  rrreasi/r-rd 
Size. 


A/ofe;  Pror/c/e   a//  ex/e/anarfory  /or/si f/ny. 


PLATED 


57 


f?ound    Gofh/c    W/nc/ow.    (construct/on) 


Vofe  :  Orntf    c/tmensfons     and   cor? sfrtsctto n  fines  •   see  fo//oiv/f-ia 


PLAT£\      I 


58 


Goffr/'c 


/Vo/e  :  /f  ef.es/ree/,  //>?/  y/ass  part  /n  f/'yht  blue,   wood   in    brown    co/or. 


59 


:  Omit  dimensions   and  consfrucf/on   lines,  see  /o//ow/r?ff 


PLATED 


60 


§ 

,lj 


PLA7£\      I 


61 


Round  Gothic    Window.   (  cons  frc/cf  ion} 


/Vote  :   Omtt   ctimens/ons     crr-rcf 


//neSj     see  fo//  owing    page 


PLATE  \       I 


Rot/no/    Gothic 


/Vofe  •    //  c/e5/recf>  ///•?/  g/ass  f>arf  in   //yhf  blue t     wooc/  /r>  brown    co/or. 


PLATE\      I 


63 


Ba/usfrac/e 


Cross   •Sacf/on  afA-B. 


A/off  ••  Omit  dim  ens/on  s;  pror/de  cross  fecf/on  fines  as  showrt.    l/se  sca/e:   /^" '=  /foot. 


64 


'* 

1 

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r 

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1 

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A  A 

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\ 

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p- 

fc 

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^ 

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s 

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Note 


c//mer>s/ons    crr7c/  cosisfri/cfrori  /ines;    see*  /~p//owfr>ff   page. 


PLATE 


65 


EF 

&a 


Note  •  //  tfes/recf  y/ve  /e//ers    er //a/  //>?/,    ffre  b/ac*  f>arf  a  darker  tone 


66 


Ge  om  efr/c  a/ 
Po/yffon  and   C/rc/e 

Data                    •'.  ;         •  •   ;';•'/;'-;  ;.'•', 
C/'rci/mference  and  Areas    o/  Ctrc/es 

H'  of 

\ 

Diam  of 

Length      of     j  ide 
Po/ygon 

D  /am.  o_f 
insert  tord 
Ci  rc/e 

To  find  Circumference  multiply  D/am.  by  3.14/6 

To  find  Area  mi//tip>/y  ^yuare  of  D;om.by  .7834 

Paly 
fan 

\ 

Otam   of 

O,<?rr7    of 

Tab/e  o/  Decimal  Fyv/ra/enfs  o/  /  *£  ",£>"&  g?" 

yon 

Circ  le 

Po/ygon 

C/rc/e 

3 

0.8  6  SO 

/.  /  S47 

*)   O  4  330 

2. 

8/hs. 

'ft   =.93  7J" 

j{  =.96S7S 

&  =.*a<J7-S 

4 

O.   7O7  / 

f,  4/42 

\    /. 

3**, 

ff*,r» 

g  =.S/J6ZS 

J 

G 

O.SS78 

\  /.70/3 

^  /.  7205 

S  =JZS 

g  =.54687S 

6 

^Q.SOOO 

\z.oooo 

\  2  S98I 

\  /.  /  S4  7 

/  _    9  f- 

^=.03/2f 

£  =.0/S623 

g  =..S7S/S5 

7 

\ 

0.438  / 

\  2.  3  OZ& 

>  3.  633  9 

S  /.  /  099 

#  =37S 

£   =.0937  f 

£  =.O4667S 

^  =.6  09  37  S 

8 

1 

0.3827 

4  2.  6  /3/ 

'  4.8Z&4 

\  t.  0824 

4  =.50 

£  =./S6ZS 

£,-.078123 

%i  =.640625 

£> 

0 

: 

0.3  4  ZO 

\Z  9  Z38 

i  6.  /  8/8 

*  /.  O642 

.j=.62S 

*   -2/S7S 

f,  =.109375 

^=.67/875 

/O 

OJ  OSO 

\3.Z36I 

<  7  6942. 

\  t   OS/  5 

lf  =  7S 

h=.Z8/Zf 

i,  =./*OffZ5 

^=.703/25 

// 

k 
c 
s 

O.28/  B 

\3.f49J 

J    9.  36  S  6 

1C  /.O422. 

y  =  .87S 

&=.3437S 

f,  =./7/  875 

42  =.7J4J7ff 

/<? 

if 

O2  S'SS 

\  3  8  637 

^//  I  963 

1  /.  O3  S3 

/fffhs. 

^  =.40625- 

«  -=.203/25 

0  =.76S62S 

/3 

t 

02.393 

*  4.  /  786 

x  /3.  /  SS6  J;  /  O2  99 

'N                                   \  ^ 

&^.4687S 

//  =.  23437S 

%f  =.7ff687S 

S-4 

»  O  ZZZ-S 

\4.  4  340 

\/.02S7 

r6  ^-.O<S2S 

g=.S}/£S- 

%,=.26S6ZS 

fj  =.828/£f 

/J 

\  O.Z  079 

\4.  8  097 

*/7  6424 

I/.  02  23 

Ji,=./97S 

%  =.S937S 

^  =296875 

g=.85937ff 

/6 

Q 

0.  tffS/ 

J  S.  /  Z3B 

\2O.  /  O94 

1/0,96 

ft  =J/2S 

Ji   =.6S6ZS 

%    =32B/2f 

j$  =.d9O6ZS 

/? 

S  O./8  33 

*.S.  4422 

^  22.  7  3  S3 

S./.0/73 

J(  =.437S 

£  =.7/  87S 

j$   =.S  S9  37  5 

J3  =.92/S7S 

/8 

%0./736 

\S.  7S88 

\25S2O8 

Z  /.  0  /S4 

%  -=.S6ZS 

'A  =78/23- 

%4  =.  3  9  06  2  S 

^   =.9f3/2f 

/£> 

^  O.I  646 

\6.  0  7J5 

\28.46  S2 

|  /.  O  /38 

fi  =.&S7S 

,Y  =.8437  f 

g  =->2/87S 

H   =.<>a+37S 

20 

1 

0  /S64 

^  6.39S.S 

^3I.S688 

5  /  .0  /  2  J 

ft-  0/23 

y  =.g06zs 

H  =4S3,2S 

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